1. 2x + 3y = 1470
3y = -2x + 1470
y = -2/3x + 490 <== slope intercept form
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2. y = -2/3x + 490....slope = -2/3.....y int = (0,490)
to graph, start at (0,490)....since the slope is -2/3, we will go down 2 spaces, then to the right 3 spaces, then down 2 spaces, and to the right 3 spaces. It helps to find the x int which can be found by subbing in 0 for y into the equation and finding x. So ur x int is (735,0)...this is where ur line should cross the x axis.
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3. function notation : f(x) = -2/3x + 490...not sure how to explain the meaning...sorry
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4. graph the function....it will be the same line as the graph I explained before...y = -2/3x + 490
y int = (0,490)
x int = (735,0)
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5. original : new :
2x + 3y = 1470 2x + 3y = 1593
3y = -2x + 1470 3y = -2x + 1593
y = -2/3x + 490 y = -2/3x + 531
similarities : Both of these equations will have the same slope, which is -2/3. Both lines are descending. Both lines are parallel to each other.
differences : These lines will have different x and y intercepts
y = -2/3x + 490 : y int = (0,490), x int = (735,0)
y = -2/3x + 531 : y int = (0,531), x int = (796.5,0)
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6. pick 2 points on the line.....(0,300) and (450,0)
find the slope using the slope formula : slope = (y2 - y1) / (x2 - x1)
(0,300)....x1 = 0 and y1 = 300
(450,0)...x2 = 450 and y2 = 0
now we sub and find the slope
slope = (0 - 300) / (450 - 0) = -300/450 reduces to -2/3
now we use y = mx + b
slope(m) = -2/3
use either of ur points...(450,0)...x = 450 and y = 0
now sub and find b, the y int
0 = -2/3(450) + b
0 = - 300 + b
300 = b
so ur equation is : y = -2/3x + 300....or 2x + 3y = 900
